SOLUTION: Determine the best method to solve each system of equations. Then solve the system.
2x+y=3x-15
x+5=4y+2x
I have (18 1/3, -3 1/2)
Is this correct. Thanks
Algebra.Com
Question 70698: Determine the best method to solve each system of equations. Then solve the system.
2x+y=3x-15
x+5=4y+2x
I have (18 1/3, -3 1/2)
Is this correct. Thanks
Found 2 solutions by bucky, checkley75:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Your answer is incorrect. Maybe I can help you to find your error. Let's begin by simplifying
the two equations a little.
.
The first equation is . You have two terms that contain x. Let's move
the x from the right side by adding -3x to it. This cancels the +3x on the right side. However,
if you add -3x to the right side, you must also add -3x to the left side. When you do that
you add the -3x to the +2x that is already on the left side. The result is -x. So the first
equation is reduced to:
.
.
That's a little easier to work with. Now let's go to work on the second equation:
.
.
Notice the right side has only terms with variables. Let's move them to the left side so
the equation has all the terms containing x and y on the left side just like the first
equation does. Let's first add -2x to both sides. On the right side the -2x cancels
the +2x so the +2x disappears. And on the left side you add the -2x to the +x to get the
sum of -x. Now add -4y to the right side term of +4x. When you do the 4x is canceled and
you are left with zero on the right side. There is no y term on the left side so when we
add -4y that term appears on the left side unchanged. At this point the second equation is:
.
.
Notice now that the +5 should be on the right side instead of the left side. Move this
term to the right side by adding -5 to both sides. The -5 adds to the +5 on the left side
and it cancels it out. On the right side when we add -5 to 0 the result is -5. So finally
we are at the point of knowing that the second equation is:
.
.
Now we are at the point of saying that our set of two equations has been changed to:
.
.
To eliminate the x term we can subtract the second equation from the first equation.
(If you prefer you can think of multiplying the entire second equation by -1 and then adding
it to the first equation.) As a result of this subtraction, the x terms disappear.
The y term of the answer is 5y and the numbers on the right side subtract to give an
answer of -10. We are left with:
.
.
which we can solve by dividing both sides by 5 to get
.
Now knowing that y = -2, we can return to either of the original equations and substitute
-2 for y. Then we can solve for x. Let's return to the original first equation of:
.
.
When we substitute -2 for y in this equation, the equation becomes:
.
.
Then we can add +2 to both sides. Following that we add -3x to both sides. Do you see why?
The resulting equation is:
.
.
Since we are to solve for +x, we can do so by multiplying both sides by -1 to get:
.
.
In summary the answers are and
.
Hopefully this will help you to understand the problem and to track down your errors.
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
2x+y=3x-15
y=3x-2x-15
y=x-15 line formula
x+5=4y+2x
4y=x-2x+5
4y=-x+5
y=-x/4+5/4 line formula
solution by graphing
(graph 300x200 pixels, x from -6 to 20, y from -20 to 20, of TWO functions y = x -15 and y = -x/4 +5/4).
solution mathematically:
y=x-15 now substitute (x-15) for y in the other formula thus:
x-15=-x/5+5/4
x+x/5=5/4+15
6x/5=5/4+60/4
6x/5=65/4 now cross multiply
6x*4=65*5
24x=325
x=325/24
x=13.54 answer now substitute 13.54 for x & solve for y.
y=13.54-15
y=-1.46 answer.
RELATED QUESTIONS
Determine the best method to solve each system of equations. Then solve the system.
y=2x
(answered by Alan3354)
determine the best method to solve each system of equations. then solve the system.... (answered by jim_thompson5910)
Determine the best method to solve the system .Then solve for x and y.
2x+y=3x-15... (answered by checkley71)
Determine the best method to solve the system .Then solve for x and y.
2x+y=3x-15... (answered by ptaylor)
solve each system of equations by using the substitution method.
{3x + 4y = 18
{ (answered by Edwin McCravy)
Determine the best method to solve the system of equations; then solve the system... (answered by stanbon)
Determin the best method to solve the system of equations.
Then solve the system.... (answered by checkley75)
solve the system of equations using the graphing method
y-x=3... (answered by Fombitz)
1.Use the Substitution method to solve the system of equations.
x + y = 10
y = x +... (answered by jim_thompson5910)